# Exponential Odds

<figure><img src="/files/RGxlEe8Qq43WRN7ZCI2g" alt=""><figcaption></figcaption></figure>

*Given our assumption that p > q, the probability drops exponentially as the number of blocks the attacker has to catch up with increases. With the odds against him, if he doesn't make a lucky lunge forward early on, his chances become vanishingly small as he falls further behind.*

Satoshi Nakamoto, Bitcoin Whitepaper

The implications of this are profound: **an attacker who lacks sufficient hashing power** relative to the network faces an uphill battle.

Hashing machinery is highly application specific and **requires a large investment to install and operate**, making it **unlikely that an attacker simply has the excess capacity** available to them at any given moment.

Without the competitive hashing power, **odds are stacked against them**, and without a fortunate breakthrough, their chances of regaining the lead diminish rapidly.


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